局部FC-一致空间内凝聚映象的极大元和广义对策及应用(Ⅱ)

在局部FC-一致空间内,引入和研究了某些新的涉及凝聚集值映象的广义矢量拟平衡问题组.应用作者在文(Ⅰ)中对局部FC-一致空间内的凝聚集值映象得到的极大元存在性定理,在局部FC-一致空间内,对这些广义矢量拟平衡问题组的解,证明了某些新的存在性定理.这些结果改进和推广了文献中某些已知结果到局部FC-一致空间.     

局部FC-一致空间内具有联立广义矢量拟平衡组约束的数学规划(英文)

在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理.     

FC-空间内的广义拟变分包含(不包含)问题组

应用丁协平在FC-空间内对集值映象证明的极大元存在性定理,在没有凸性结构的FC-空间内对广义拟变分包含(不包含)问题组的解证明了某些新的存在性定理.这些结果在较弱的条件下改进和推广了最近文献中的某些结果从拓朴矢量空间的闭凸子集到FC-空间.     

乘积FC-空间内涉及一较好容许集值映象的优化映象族的极大元及其应用

引入了涉及一较好容许集值映象的映一拓扑空间到一有限连续拓扑空间(简称,FC-空间)的优化映象族.在乘积FC-空间的非紧设置下对这类优化映象族证明了某些极大元存在性定理.在乘积FC-空间内给出了对不动点和极小极大不等式组的应用.这些定理改进、统一和推广了最近文献中的很多重要结果.     

乘积G-凸空间内的非空交定理和广义矢量平衡问题组

利用作在G凸空间内对集值映象簇得到的一个极大元存在性定理，在非紧乘积G空间内，对集值映象簇建立了某些新的非空交定理．作为应用，在非紧乘积G凸空间内，对广义矢量平衡问题组证明了一些平衡存在性定理．这些定理统一、改进和推广了献中一些重要的已知结果．     

局部 FC-一致空间内的广义约束多目标对策

在没有任何凸性结构的局部FC-一致空间内引入和研究了一类新的广义约束多目标对策,其中局中人数可以是有限或无限的和所有的支付函数可以取值于无限维空间.利用在局部FD-一致空间内得到的一个Himmelberg型不动点定理,在局部PC-一致空间内对广义约束多目标对策建立了某些弱Pareto平衡存在性定理.这些定理改进,统一和推广了最近文献中相应结果.     

乘积FC-空间内涉及——较好容许集值映象的优化映象族的极大元及其应用

引入了涉及-较好容许集值映象的映-拓扑空间到-有限连续拓扑空间（简称，FC-空间）的优化映象族．在乘积FC-空间的非紧设置下埘这类优化映象族证明了某些极大元存在性定理．在乘积FC-空间内给出了对不动点和极小极大不等式组的应用．这些定理改进、统一和推广了最近文献中的很多重要结果．     

局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

在没有凸性结构的局部FC-一致空间内,引入和研究了某些新的广义矢量拟变分包含问题组和广义矢量理想(真,帕雷多(Pareto),弱)拟优化问题组.应用KKM型定理和Himmelberg型不动点定理,首先对广义矢量拟变分包含问题组的解,证明了某些新的存在性定理.作为应用,对广义矢量理想(真,帕雷多,弱)拟优化问题组的解也得到了某些新的存在性结果.     

FC-空间中含伪单调集值映象的广义向量平衡问题

在FC-空间内引入和研究了几类含伪单调集值映象的广义向量平衡问题．利用第二作者的KKM定理,在FC空间内对这些广义向量平衡问题证明了平衡点的存在性定理,改进与推广了近期文献中的相应结果．     

乘积拓扑矢量空间中的不动点定理和广义矢量平衡问题组

利用零调映象的一个不动点定理,在乘积拓扑矢量空间内得到了某些新的不动点定理,作为应用,在乘积拓扑矢量空间内,对一类广义矢量平衡问题组证明了一些平衡存在性定理,这些定理推广了近期文献中的一些重要的已知结果.     

EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES

In this article,we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces.Each leader has a constrained correspondence.By using a collective fixed point theorem in locally FC-uniform spaces due to author,some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings.These results generalize some corresponding results in recent literature.     

Monotone generalized variational inequalities and generalized complementarity problems

Some existence results for generalized variational inequalities and generalized complementarity problems involving quasimonotone and pseudomonotone set-valued mappings in reflexive Banach spaces are proved. In particular, some known results for nonlinear variational inequalities and complementarity problems in finite-dimensional and infinite-dimensional Hilbert spaces are generalized to quasimonotone and pseudomonotone set-valued mappings and reflexive Banach spaces. Application to a class of generalized nonlinear complementarity problems studied as mathematical models for mechanical problems is given.The research of the first author was supported by the National Natural Science Foundation of P. R. China and by the Ethel Raybould Fellowship, University of Queensland, St. Lucia, Brisbane, Australia.     

The existence of zeros of set-valued mappings in reflexive Banach spaces

In this paper, we establish the equivalence between the existence of zeros for set-valued mappings and the solvability of variational inequality, under some conditions involving the generalized projection operator. Basing on this result, we obtain some existence theorems of zeros for quasimonotone set-valued mappings. As application, we derive several fixed point theorems for generalized inward mappings in Hilbert spaces.     

G -凸空间中的广义对策和广义矢量拟平衡问题组

该文在广义G -凸空间中引入并研究了一类新的广义矢量拟平衡问题组(SGVQEP).利用作者的一族集值映象的极大元存在定理,证明了广义对策的一个新的平衡存在定理.作为应用,在非紧乘积G -凸空间中证明了SGVQEP解的一些新的存在定理.     

Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces

A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the approximate solutions of the generalized mixed equilibrium problems (GMEP) and bilevel generalized mixed equilibrium problems (BGMEP) involving set-valued mappings is introduced. By using a minimax inequality, the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions. By using auxiliary principle technique, new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP is suggested and analyzed. Strong convergence of the iterative sequences generated by the proposed algorithms is proved under quite mild assumptions. These results are new and generalize some recent results in this field.     

Existence and iterative algorithm of solutions for a class of bilevel generalized mixed equilibrium problems in Banach spaces

A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the approximate solutions of the generalized mixed equilibrium problems (GMEP) and bilevel generalized mixed equilibrium problems (BGMEP) involving set-valued mappings is introduced. By using a minimax inequality, the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions. By using auxiliary principle technique, new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP are suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithms are proved under quite mild assumptions. These results are new and generalize some recent results in this field.     

Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces

In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author, we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature.